Leonhard Euler was one of the most prolific mathematicians of all time. This year marks the 300th anniversary of his birth. Robin Wilson starts off a four part series on Euler with a look at his life and work.

Runner up in the schools category Being good at mental arithmetic isn't going to gain you much street cred these days. But, as Owen Daniel explains, not so long ago it was a sure route to fame and fortune — even if you were a horse.

Runner up in the general public category. Great minds spark controversy. This is something you'd expect to hear about a great philosopher or artist, but not about a mathematician. Get ready to bin your stereotypes as Rebecca Morris describes some controversial ideas of the great mathematician David Hilbert.

When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled
life.

In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.